Linear transformations of tropical matrices preserving the cyclicity index-Reference-Cited by-同舟云学术

Linear transformations of tropical matrices preserving the cyclicity index

Published:2021-01-01 Issue:1 Volume:9 Page:112-118
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Guterman Alexander¹,Kreines Elena²,Thomassen Carsten³

Affiliation:

1. Faculty of Mathematics and Mechanics , Moscow State University , Moscow, GSP-1, 119991, Russia ; Moscow Center for Fundamental and Applied Mathematics , Moscow, GSP-1, 119991, Russia ; Moscow Institute of Physics and Technology, Dolgoprudny , 141701, Russia

2. Faculty of Mathematics and Mechanics , Moscow State University , Moscow, GSP-1, 119991, Russia ; Moscow Center for Fundamental and Applied Mathematics , Moscow, GSP-1, 119991, Russia

3. Department of Applied Mathematics and Computer Science , Technical University of Denmark , DK-2800 Lyngby , Denmark

Abstract

Abstract We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index. We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology,Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/spma-2020-0128/pdf

Reference11 articles.

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2. [2] J. Dieudonné, Sur une généralisation du groupeorthogonal à quatre variables, Arch. Math. 1949, 1, 282–287.

3. [3] G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineare Substitutionen, Sitzungsber, Preuss. Akad. Wiss (Berlin), Berlin, 1897, pp. 994–1015.

4. [4] A. Guterman, Matrix invariants over semirings, Handbook of Algebra ed.: M. Hazewinkel, Elseiver, North-Holland, 2009, 6, 3–33.

5. [5] A. Guterman, M. Johnson, M. Kambites, Linear isomorphisms preserving Green’s relations for matrices over anti-negative semifields, Linear Algebra Appl. 2018, 545, 1–14.

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